Five times the sum of three consecutive integers is 150. what are the integers?

1 answer:

8 0

Alright! Let's start off with the basic from the info given:

150= 5(x+y+z)
First off, since you're looking for x y and z, let's divide both sides by 5:
30= x+y+z

Now let's change y and z written in terms of x:
y= x+1 because it's a consecutive integer
z=x+2 because it's 1 + the value for y

So let's set this up:
30= x + x+1 +x+2

Then simplify
30= 3x + 3

Since you're looking for x, let's subtract 3 then divide by 3
27= 3x
9=x

Now that you have the value of x, plug it into the equations above for y and z:
y=x+1
y= 9+1=10

z= x+2
z= 9+2 =11

Try it out!

(9+10+11) * 5 = 150
(30) * 5 = 150

150 = 150!

So you have x= 9, y= 10, and z=11

Hope this helps!

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Which equation represents the polynomial function with zeros −1, 1, and 3 (multiplicity of 2), and a y-intercept of −18? (4 poin

Vlad [161]

Correct Answer:
3rd option is the correct answer

Solution:
The zeros of the polynomial are -1,1 and 3. The multiplicity of 3 is 2. So the polynomial can be expressed as:

$y=a (x-3)^{2}(x-1)(x+1)$

The y-intercept of the polynomial is -18. This means the polynomial passes through the point (0,-18). Therefore, y must be -18 when x = 0. Using these values of x and y in previous equation we get:

$-18=a (0-3)^{2}(0-1)(0+1) \\ \\ 
-18=-9a \\ \\ 
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The final equation of the polynomial becomes:

$y=2 (x-3)^{2}(x-1)(x+1)$

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

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